$\dfrac{ -3c + d }{ -6 } = \dfrac{ 5c + 5e }{ 7 }$ Solve for $c$.
Answer: Multiply both sides by the left denominator. $\dfrac{ -3c + d }{ -{6} } = \dfrac{ 5c + 5e }{ 7 }$ $-{6} \cdot \dfrac{ -3c + d }{ -{6} } = -{6} \cdot \dfrac{ 5c + 5e }{ 7 }$ $-3c + d = -{6} \cdot \dfrac { 5c + 5e }{ 7 }$ Multiply both sides by the right denominator. $-3c + d = -6 \cdot \dfrac{ 5c + 5e }{ {7} }$ ${7} \cdot \left( -3c + d \right) = {7} \cdot -6 \cdot \dfrac{ 5c + 5e }{ {7} }$ ${7} \cdot \left( -3c + d \right) = -6 \cdot \left( 5c + 5e \right)$ Distribute both sides ${7} \cdot \left( -3c + d \right) = -{6} \cdot \left( 5c + 5e \right)$ $-{21}c + {7}d = -{30}c - {30}e$ Combine $c$ terms on the left. $-{21c} + 7d = -{30c} - 30e$ ${9c} + 7d = -30e$ Move the $d$ term to the right. $9c + {7d} = -30e$ $9c = -30e - {7d}$ Isolate $c$ by dividing both sides by its coefficient. ${9}c = -30e - 7d$ $c = \dfrac{ -30e - 7d }{ {9} }$